Priya mixes 2 1/2 cups of water with 1/3 cup of orange juice concentrate. diego mixes 1 2/3 cups of water with 1/4 cup orange juice concentrate. how much concentrate should each of them mix with 100 cups of water to make juice that tastes the same as their original recipe? explain or show your reasoning.



Priya needs 13⅓ cups of orange juice

Diego 15 cups

Step-by-step explanation:

Priya

Cup of water = 2½

Cup of orange = ⅓

If 2½ cups of water requires ½ cup of orange juice concentrate

Then 100 cups of water would require x cup of orange

Representing the above statement mathematically

2½ : ⅓ = 100 : x

5/2 : 1/3 = 100 : x Convert ratio sign to division

5/2 ÷⅓ = 100/x

5/2 * 3 = 100/x

15/2 = 100/x Multiply both sides by x

15/2 * x = 100/x * x

15x/2 = 100 Multiply both sides by 2

2 * 15x/2 = 2 * 100

15x = 200 Divide both sides by 15

x = 200/15

x = 13⅓

So, 13⅓ cups of orange is needed by Priya

Diego

Cup of water = 1⅔

Cup of orange = ¼

If 1⅔ cups of water requires ¼ cup of orange juice concentrate

Then 100 cups of water would require x cup of orange

Representing the above statement mathematically

1⅔:¼ = 100:x

5/3 : ¼ = 100:x

5/3 ÷¼ = 100 ÷ x

5/3 * 4/1 = 100 ÷ x

20/3 =100/x Multiply x to both sides

20/3 * x = 100/x * x

20x/3 = 100 Multiply 3 to sides by 3

3 * 20x/3 = 100 * 3

20x = 300 Divide both sides by 2

20x/20 = 300/20

x = 15

So, 15 cups of orange is needed by Diego

366

step-by-step explanation:

77

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